共查询到17条相似文献,搜索用时 710 毫秒
1.
By considering (2+1)-dimensional non-isospectral discrete zero curvature equation, the (2+1)-dimensional non-isospectral Toda lattice hierarchy is constructed in this article. It follows that some reductions of the (2+1)- dimensional Toda lattice hierarchy are given. Finally, the (2+1)-dimensional integrable coupling system of the Toda lattice hierarchy is obtained through enlarging spectral problem. 相似文献
2.
In this paper, we extend a (2+2)-dimensional continuous zero curvature equation to (2+2)-dimensional discrete zero curvature equation, then a new (2+2)-dimensional cubic Volterra lattice hierarchy is obtained. Fhrthermore, the integrable coupling systems of the (2+2)-dimensional cubic Volterra lattice hierarchy and the generalized Toda lattice soliton equations are presented by using a Lie algebraic system sl(4). 相似文献
3.
In this paper,we focus on the construction of new(1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra A 1.By designing two new(1+1)-dimensional discrete spectral problems,two new discrete integrable systems are obtained,namely,a 2-field lattice hierarchy and a 3-field lattice hierarchy.When deriving the two new discrete integrable systems,we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy.Moreover,we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity. 相似文献
4.
JIANG Qiao-Yun ZHOU Ru-Guang 《理论物理通讯》2006,46(5):773-778
A new (29-1)-dimensional lattice equation is presented based upon the first two members in the hierarchy of the combined Toda lattice and relativistic Toda lattice (TL-RTL) equations in (19991) dimensions. A Darboux transformation for the hierarchy of the combined TL-RTL equations is constructed. Solutions of the first two members in the hierarchy of the combined TL-RTL equations, as well as the new (29-1)-dimensional lattice equation are explicitly obtained by the Darboux transformation. 相似文献
5.
An integrable (2+1)-dimensional coupled mKdV equation is decomposed into two (1 +1)-dimensional soliton systems, which is produced from the compatible condition of three spectral problems. With the help of decomposition and the Darboux transformation of two (1+1)-dimensional soliton systems, some interesting explicit solutions of these soliton equations are obtained. 相似文献
6.
DAI Chao-Qing YAN Cai-Jie ZHANG Jie-Fang 《理论物理通讯》2006,46(3):389-392
In this paper, the entangled mapping approach (EMA) is applied to obtain variable separation solutions of (1+1)-dimensional and (3+1)-dimensional systems. By analysis, we firstly find that there also exists a common formula to describe suitable physical fields or potentials for these (1+1)-dimensional models such as coupled integrable dispersionless (CID) and shallow water wave equations. Moreover, we find that the variable separation solution of the (3+1)-dimensional Burgers system satisfies the completely same form as the universal quantity U1 in (2+1)-dimensional systems. The only difference is that the function q is a solution of a constraint equation and p is an arbitrary function of three independent variables. 相似文献
7.
We study the Painlevé property of the (1+1)-dimensional equations arising from the symmetry reduction for the (2+1)- dimensional ones. Firstly, we derive the similarity reduction of the (2+1)-dimensional potential Calogero-Bogoyavlenskii- Schiff (CBS) equation and Konopelchenko-Dubrovsky (KD) equations with the optimal system of the admitted one-dimensional subalgebras. Secondly, by analyzing the reduced CBS, KD, and Burgers equations with Painlevé test, re-spectively, we find both the Painlevé integrability, and the number and location of resonance points are invariant, if the similarity variables include all of the independent variables. 相似文献
8.
WANG Yi-Hong WANG Sheng-Kui 《理论物理通讯》2008,50(8):299-302
In this paper, with the aid of symbolic computation, we present a uniform method for constructing soliton solutions and periodic solutions to (2+1)-dimensional Toda lattice equation. 相似文献
9.
The (2+1)-dimensional nonlinear SchrSdinger (NLS) equation with spatially inhomogeneous nonlinearities is investigated, which describes propagation of light in (2+1)-dimensional nonlinear optical media with inhomogeneous nonlinearities. New types of optical modes and nonlinear effects in optical media are presented numerically. The results reveal that the regular split of beam can be obtained in (2+1)-dimensional nonlinear optical media with inhomogeneous nonlinearities, by adjusting the guiding parameter. Furthermore, the stability of beam regular split is discussed numerically, and the results reveal that the beam regular split is stable to the finite initial perturbations. 相似文献
10.
A 2+1-dimensional discrete is presented, which is decomposed into a new integrable symplectic map and a class of finite-dimensional integrable Hamiltonian systems, with aid of the nonlineaxization of Lax pairs. The system is completely integrable in the Liouville sense. 相似文献
11.
《理论物理通讯》2017,(12)
Two new shift operators are introduced for which a few differential-difference equations are generated by applying the R-matrix method. These equations can be reduced to the standard Toda lattice equation and(1+1)-dimensional and(2+1)-dimensional Toda-type equations which have important applications in hydrodynamics, plasma physics, and so on. Based on these consequences, we deduce the Hamiltonian structures of two discrete systems. Finally,we obtain some new infinite conservation laws of two discrete equations and employ Lie-point transformation group to obtain some continuous symmetries and part of invariant solutions for the(1+1) and(2+1)-dimensional Toda-type equations. 相似文献
12.
A new (2+1)-dimensional lattice equation is presented based upon
the first two members in the hierarchy of the combined Toda lattice and relativistic Toda lattice (TL-RTL)
equations in (1+1) dimensions. A Darboux transformation for the hierarchy
of the combined TL-RTL equations is constructed. Solutions of the first two members in the hierarchy of the
combined TL-RTL equations, as well as the new (2+1)-dimensional lattice
equation are explicitly obtained by the Darboux transformation. 相似文献
13.
本文推广了双曲函数方法用于求解非线性离散系统。求解离散的(2+1)维Toda系统和离散的mKdV系统,成功地得到了离散钟型孤立子、离散冲击波型孤立子及一些新的精确行波解。 相似文献
14.
Based upon Cartan's geometric formulation of differential equations, Harrison and Estabrook proposed a geometric approach for the symmetries of differential equations. In this Letter, we extend Harrison and Estabrook's approach to analyze the symmetries of differential-difference equations. The discrete exterior differential technique is applied in our approach. The Lie symmetry of (2+1)-dimensional Toda equation is investigated by means of our approach. 相似文献
15.
JIANG Qiao-Yun ZHOU Ru-Guang 《理论物理通讯》2006,46(11)
A new (2 1)-dimensional lattice equation is presented based upon the first two members in the hierarchy of the combined Toda lattice and relativistic Toda lattice (TL-RTL) equations in (1 1) dimensions. A Darboux transformation for the hierarchy of the combined TL-RTL equations is constructed. Solutions of the first two members in the hierarchy of the combined TL-RTL equations, as well as the new (2 1)-dimensional lattice equation are explicitly obtained by the Darboux transformation. 相似文献
16.
《Physics letters. A》1987,125(5):247-249
We present a Darboux transformation for the (2 + 1)-dimensional integrable Toda lattice and use it to construct the one-soliton solution. 相似文献
17.
In this paper, with the aid of symbolic computation, we present a
uniform method for constructing soliton solutions and periodic
solutions to (2+1)-dimensional Toda lattice equation. 相似文献